What is the value of sin(arctan(-sqrt(3))) ?

The value of sin(arctan(-sqrt(3))) is -(sqrt(3))/2

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sin(arctan(-sqrt(3)))

sin (arctan (- 3))

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

sin (arctan (- 3))

Rewrite using trig identities:

sin (arctan (- 3)) = \frac{( - 3 ) 1 + ( - 3 ) ^{2}}{1 + ( - 3 ) ^{2}}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( - 3 ) 1 + ( - 3 ) ^{2}}{1 + ( - 3 ) ^{2}}

= \frac{( - 3 ) 1 + ( - 3 ) ^{2}}{1 + ( - 3 ) ^{2}}

Simplify

= - \frac{3}{2}

cos (- 22 5^{\circ})

arctan (\frac{2}{2 3})

cos (45 0^{\circ})

sec (- \frac{3 π}{4})

arcsec (3)

What is the value of sin(arctan(-sqrt(3))) ?
The value of sin(arctan(-sqrt(3))) is -(sqrt(3))/2